VIII International Scientific Colloquium

Modelling for Materials Processing

Riga, September 21 - 22, 2017

Analysis of the Impact of Modification of Cold Crucible Design on

the Efficiency of the Cold Crucible Induction Furnace

R. Przylucki, S. Golak, P. Bulinski, J. Smolka, M. Palacz, G. Siwiec,

J. Lipart, L. Blacha

Abstract

The article includes numerical simulation results for two cold crucible induction

furnaces (CCIF). Induction furnaces differ in cold crucible design, while the inductor

geometry was preserved for both variants. Numerical simulations were conducted as three

dimensional one, with coupled analysis of electromagnetic, thermal and fluid dynamics fields.

During the experiment, six calculation variants, differ in amount of molten titanium (three

different weights of titanium for each type of cold crucible) were considered. Main parameters

controlled during the calculations were: electrical efficiency of the CCIF and the meniscus

shape of liquid metal.

Introduction

Induction furnaces with cold crucible are most commonly used for melting very

reactive metals and alloys. Such metals should be melted without contact with the crucible.

Cold crucible is a compromise solution. The best, from the point of view of lack of contact, is

the levitation melting. But in levitation melting there are problems with the lifting force

especially for heavy workpieces. In cold crucible furnace, the molten metal contacts only with

a bottom of the crucible. From the crucible walls, liquid metal is repulsed by electrodynamic

forces. At the bottom, the metal is in contact with the crucible not directly, but through a

solidified layer (skull). There are two main problems in cold crucible furnaces design: electric

(and of course total) efficiency, and minimization of the skull [1].

Low electric efficiency is due to double conversion of electrical energy: from current

to the electromagnetic field and again to current. First conversion between inductor and cold

crucible segment (finger) and the second between cold crucible segments and the molten

metal. This cannot be changed but energy losses can be reduced by the appropriate cold

crucible construction [2]. Moreover, the skull volume depends on the cold crucible

construction.

The aim of the article is the modification of the design of cold crucible to improve the

efficiency of the melting process and to minimize the skull.

1. Models of considered cold crucibles

Two cold crucible designs are investigated in this article. Simplified sketch of the first

and the second construction is presented in Fig. 1 and 2, respectively. As shown in Figure 1

first construction was made from one piece of copper. There is a separation between

segments, and the incision also includes part of the crucible bottom (shaded part with index

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doi:10.22364/mmp2017.11

6). There is a massive chassis below the inductor. The shuns does not have pole pieces. The

crucible bottom is slightly concave. Advantage of this design is the incision of the outer part

of bottom which prevents shorting of the currents induced in the bottom part of the segments.

Disadvantages of this construction are: massive chassis just below the inductor, and lack of

pole pieces. Problematic is also the recess in the bottom. This causes a thick skull.

The second construction of the cold crucible, considered in this article, consists of two

main, separate pieces: segments and flat bottom. The shunts has pole pieces below the

inductor, and there is no conducting material just below inductor and segments. Such a design

(more difficult from the construction point of view) prevents the induction of currents outside

the cold crucible segments.

Fig. 1. Sketch of first CCIF Model, 1 – metal melt, 2 – solid bottom, 3 – segment, 4 –

inductor, 5 – shunt, 6 – separated part of the bottom

Fig. 2. Sketch of second CCIF Model, 1 – metal melt, 2 – solid bottom, 3 – segment, 4 –

inductor, 5 – shunt, 6 – ceramic element

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Basic dimensions of the models

are presented in Table 1. Bottom and

segments of crucible were made of

copper of the conductivity of 56E6 S/m,

melt metal was made of titanium with

the conductivity of 50.5E4 S/m. Shunts

were made of Fluxtrol 100.

The problem was considered as

coupled analysis of: electromagnetic,

thermal and fluid dynamics fields in 3-

D domain. Electromagnetic field

analysis was performed with use of

getDP program. For the temperature

and fluid dynamics analysis, Ansys-

Fluent program was used.

1.2. Model for electromagnetic field analysis

Analysis of electromagnetic field basis on A-V formulation (1) [3] is conducted as a

steady state one. Electromagnetic field analysis results were volumetric heat sources (2) [4]

and volumetric electromagnetic forces (4) [4]. These values were calculated in the melt area

only, and they are input data for temperature and fluid dynamics analysis.

0gradjrot1

μ

1rot

0

VAσA

μ (1)

where:

0 - permeability of vacuum; r- relative permeability; A - magnetic vector potential; -

conductivity; - angular velocity; V - scalar electric potential.

1

2

1 2 Jvq (2)

Vgradj AσJ (3)

where:

qv - volumetric density of active power; J - current density.

*Re2

1BJf m

(4)

AB rot (5)

where:

fm - average for period volumetric force density; B* - conjugate value of induction.

Tab. 1. Model parameters

Parameter (unit) Model 1 Model 2

rbw (mm) 40 45

sbi (mm) 6 1

sf (mm) 15 15

gs (mm) 2 2

ss (mm) 10 10

si (mm) 13 13

ri (mm) 75 75

rt (mm) 90 -

hbi (mm) 4 10

hb (mm) 10 10

hs (mm) 85 85

hp (mm) - 7,5

hf (mm) 144 144

hsc (mm) 13 13

hlc (mm) 25 25

hcc (mm) 4 4

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For EM field calculation, only 1/16 of the device

was modelled (Fig. 3). It was possible because of

periodicity of the device construction.

On front and back model surfaces (Fig. 3), the

periodicity boundary condition was applied. In other

directions, the computational model is surrounded by air

and on the outside air surfaces boundary Dirichlet

condition setting potentials to zero was applied.

1.3. Model for temperature field and fluid dynamics

analysis

Analysis of temperature field and fluid dynamics

were performed in Ansys Fluent program. The calculation

domain was limited to the melt area and a bottom of

crucible only, as presented in Fig. 4. Temperature

calculations were based on equation (6) [5]:

rv qqTkTcTct

graddivgradv (6)

where:

- density; c - specific heat; T - temperature; v – velocity vector; k - thermal conductivity; qv -

volumetric heat source from electromagnetic calculation; qr - volumetric density of radiative

heat exchange.

As in the case of electromagnetic field analysis, the

calculation domain was limited to 1/16 of the device (Fig.

4). On the front and back model surfaces adiabatic

boundary condition was applied, on the outside surface in

the crucible segments and below bottom (out 1, Fig. 4.)

Dirichlet boundary condition setting temperature to 303 K

was applied, on the free molten metal surface (out 2), the

heat loss with convection and radiation were taken into

consideration.

The fluid dynamics calculations should determine

the shape of free surface of molten metal in the CCIF and

therefore the flow field within crucible was treated as

multiphase one. The Volume of Fluid approach was

applied in the calculation model. To obtain the flow field

distribution, the continuity equation in the form (7) [5] and

momentum conservation equation (8) [5] should be solved.

vqqqqt

div

(7)

where: q - volume fraction of the qth phase; q - density of the qth phase.

sm ffpt

gvvvvv rotrotdivgradgraddiv (8)

where: p - pressure; - dynamic viscosity; g - gravitational acceleration; fs - surface tension

force.

Fig. 3. Calculation model for EM

field analysis of the first CCIF

Fig. 4. Calculation model for EM

field analysis of the first CCIF

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These equations are supplemented with boundary condition, on the front and back

surfaces periodicity boundary condition was assumed. On the top of model pressure outlet

condition was adopted, for the free surface of molten metal shear stress equal to 0 on both

sides was assumed. On the outside wall of the model (out 2), no slip condition was assumed.

1.4. Coupling procedure

Electromagnetic, heat transfer and fluid flow calculation were conducted for two

different numerical submodels. Models differs in geometry and calculation domain.

Calculation model for electromagnetic field consists of molten metal, crucible, inductor, shunt

and air. Temperature and FD calculations were conducted for the model limited to the molten

metal and air above free surface of metal, and bottom of the crucible.

Fluid dynamics and temperature calculations were performed in time domain, and the

time step was 0.00001 s. Each 25 time steps the calculations of electromagnetic field were

performed and mean for the period values of forces and power sources were determined, and

then transferred as the source terms for the thermal submodel. Before the transfer, the forces

and heat sources from EM calculation were approximated for the T-FD calculation mesh [6].

2. Numerical experiment

Six simulation variants were performed during the experiment. For each of the two

CCIF models, three calculation variants, different in volume of the titanium, were conducted.

The variant designators are as follows: CCIF model 1, volume of titanium 1 is designated as

m1v1. Considered quantities of titanium are: 1,06 kg, 1,6 kg, 2,13 kg which corresponds to

complete filling the crucible to the level of 0,04 m (27%), 0,06 m (42%), 0,08 m (55%).

All variants of calculations were conducted for the same inductor current and current

frequency of 10 kHz. The liquid metal properties were as follows: conductivity [5] = 50,5E4

S/m density [6] = 4160 kg/m3, thermal conductivity [7] λ= 32 W/(mK), specific heat c =

9,87E2 J/(kg K), dynamic viscosity [8] = 4,03E-3 Pa s.

References [1] Spitans S., Baake E.., Jakovics A., Franz H.: Numerical simulation of electromagnetic levitation in cold

crucible furnace. Magnetohydrodynamics Vol. 51 (2015), no. 3 pp. 567-578.

[2] Rot D., Jirinec S., Kozeny J., Poznyak I.: Electrical efficiency of induction furnace with cold crucible via

different segments width. Electric Power Engineering (EPE) 2015 16 th International Conference IEE DOI

10.1109/EPE.2015.7161132 (IEE Xplore 2.06.2017).

[3] Fort J., Garnich M., Klymyshyn N.: Electromagnetic and thermal-flow modelling of a cold-wall crucible

induction melter. Metallurgical and Materials Transaction B, Vol. 36, 2005, pp. 141-152.

[4] Flux 3D Vol5 Complement on the formulations 3D. Cedrat 2005, pp. 138-171.

[5] Ansys 15.0 manual, www.ansys.com.

[6] Bulinski P., Smolka J., Golak S., Przylucki R., Palacz M., Siwiec G., Lipart J., Bialecki R., Blacha L.:

Numerical and experimental investigation of heat transfer process in electromagnetically driven flow within

vacuum induction furnace. Applied Thermal Engineering, Vol. 124 (2017), pp. 1003 - 1013.

[6] Seydel U., Fucke W.: Electrical resistivity of liquid Ti, V, Mo and W. Journal of Physics F: Metal Physics

Vol. 10, 1980.

[7] Ishikawa T.: Thermophysical properties of molten refractory metals measured by an elecrostatic levitator.

Journal of Electric Materials, 2005.

[8] Mills K.C., Monaghan B.J., Knee J.: Thermal conductivities of liquid metals. Proceedings of the Twenty-

Third International Thermal Conductivity Conference, 1996.

[9] Pardis P.-F, Ishikawa T., Yoda S.: Non contact measurements of surface tensions and viscosity of niobium,

zirconium and titanium using and electrostatic levitation furnace. International Journal of Thermophysics

Vol. 23. no 3, 2002.

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Authors Roman Przylucki, Ph.D., D.Sc. Slawomir Golak, Ph.D., D.Sc.

Department of Industrial Informatics Department of Industrial Informatics

Silesian University of Technology Silesian University of Technology

Krasinskiego 8 Krasinskiego 8

40-019 Katowice, Poland 40-019 Katowice, Poland

E-mail: roman.przylucki@polsl.pl E-mail: slawomir.golak@polsl.pl

Piotr Bulinski, M.Sc. Jacek Smolka, Ph.D., D.Sc.

Institute of Thermal Technology Institute of Thermal Technology

Silesian University of Technology Silesian University of Technology

Konarskiego 22 Konarskiego 22

44-100 Gliwice, Poland 44-100 Gliwice, Poland

E-mail: piotr.bulinski@polsl.pl jacek.smolka@polsl.pl

Michał Palacz, Ph.D. Grzegorz Siwiec, Ph.D., D.Sc.

Institute of Thermal Technology Institute of Metals Technology

Silesian University of Technology Silesian University of Technology

Konarskiego 22 Krasinskiego 8

44-100 Gliwice, Poland 40-019 Katowice, Poland

E-mail: michal.palacz@polsl.pl E-mail: grzegorz.siwiec@polsl.pl

Jakub Lipart, Ph.D. Leszek Blacha, Prof.

Institute of Metals Technology Institute of Metals Technology

Silesian University of Technology Silesian University of Technology

Krasinskiego 8 Krasinskiego 8

40-019 Katowice, Poland 40-019 Katowice, Poland

E-mail: leszek.blacha@polsl.pl E-mail: leszek.blacha@polsl.pl

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